The significant importance of graph coloring motivates various advancements in modern algorithms aimed at tackling both practical and real-world problems in computer science. Meta-heuristic and evolutionary algorithms offer insightful and favorable solutions for most Graph Coloring Problem (GCP) instances. However, currently, no algorithm possesses the strength to generate optimal colorations for all frequently used graph instances. This manuscript presents a comprehensive analysis of performance comparison between Differential Evolution Algorithm (DEGCP) and Gravitational Search Algorithm (GSAGCP) to emphasize the utilization of optimization algorithms in addressing the challenges posed by GCP in a single framework. The experimental outcomes show that the DEGCP algorithm performs better than the GSAGCP algorithm for some widely used benchmark graph instances.